diff --git a/sympy/functions/elementary/integers.py b/sympy/functions/elementary/integers.py
index fa68122865..691f178172 100644
--- a/sympy/functions/elementary/integers.py
+++ b/sympy/functions/elementary/integers.py
@@ -390,13 +390,16 @@ def __ge__(self, other):
     def __gt__(self, other):
         if self.is_extended_real:
             other = _sympify(other)
-            # Check if other < 0
-            res = self._value_one_or_more(other)
-            if res is not None:
-                return not(res)
-            # Check if other >= 1
-            if other.is_extended_negative:
+            # Check if other is a positive number
+            if other.is_positive:
+                # If other is positive, ceiling of any number is greater than 0
                 return S.true
+            # Check if other is non-positive
+            if other.is_nonpositive:
+                # If other is non-positive, ceiling of any number is not greater
+                return S.false
+            # If other is not a number, return unevaluated
+            return Gt(self, other, evaluate=False)
         return Gt(self, other, evaluate=False)
 
     def __le__(self, other):
